How large dimension guarantees a given angle?

Details How large dimension guarantees a given angle? How large dimension guarantees a given angle?

2011-01-07

arxiv.org/abs/1101.1426v2

Mathematics

Classical Analysis and ODEs

Scientific paper

We study the following two problems: (1) Given $n\ge 2$ and $\al$, how large Hausdorff dimension can a compact set $A\su\Rn$ have if $A$ does not contain three points that form an angle $\al$? (2) Given $\al$ and $\de$, how large Hausdorff dimension can a %compact subset $A$ of a Euclidean space have if $A$ does not contain three points that form an angle in the $\de$-neighborhood of $\al$? An interesting phenomenon is that different angles show different behaviour in the above problems. Apart from the clearly special extreme angles 0 and $180^\circ$, the angles $60^\circ,90^\circ$ and $120^\circ$ also play special role in problem (2): the maximal dimension is smaller for these special angles than for the other angles. In problem (1) the angle $90^\circ$ seems to behave differently from other angles.

Affiliated with

Also associated with

No associations

Rating

How large dimension guarantees a given angle? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with How large dimension guarantees a given angle?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and How large dimension guarantees a given angle? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-483889